I've had ongoing slowness, hanging/freezing and having to frequently hard reboot my venerable 32 gb 5.
Apple Store did a full reset(dfu if memory serves correctly). Said next step would be a set up as new restore instead of a restore from iCloud.
Does that sound reasonable?
Can I get back
Contacts?
iMessages?
Camera roll?
Apps?
If I do the set up as new thing?
messages will be gone if you set up as new. Pics also unless you use iCloud Photo Library. Contacts should be synced to iCloud if you have the option enabled. Apps you can just redownload, you will lose all cached data though. If you are on iOS10 then it may not matter. My old 5 is getting horrible battery life since I upgraded to 10.0